Various grating designs have been proposed by several investigators fo
r possible use with the Lyman/Far-Ultraviolet Spectroscopic Explorer m
ission. The image quality, the feasibility, and the efficiency of five
designs are compared, each using a distinct type of grating: (1) a gr
ating ruled on a deformed ellipsoidal or toroidal blank, (2) an ellips
oidal grating recorded holographically with two auxiliary spherical mi
rrors, (3) a spherical holographic grating recorded with two auxiliary
spherical holographic gratings, (4) a spherical ruled grating with va
riable spacing and straight grooves, and (5) a spherical ruled grating
with a groove pattern that is determined theoretically (hybrid gratin
g). From a purely theoretical viewpoint, grating (5) provides the fine
st images, followed by gratings, (3), (1), (4), and (2). In view of th
e current technological limitations, the order of practical importance
is gratings (4), (1), (2), (3), and (5).